The following is an extremely simplified view of how SSL is implemented and what part the certificate plays in the entire process.
Normal web traffic is sent unencrypted over the Internet. That is, anyone with access to the right tools can snoop all of that traffic. Obviously, this can lead to problems, especially where security and privacy is necessary, such as in credit card data and bank transactions. The Secure Socket Layer is used to encrypt the data stream between the web server and the web client (the browser).
SSL makes use of what is known as asymmetric cryptography, commonly referred to as public key cryptography (PKI). With public key cryptography, two keys are created, one public, one private. Anything encrypted with either key can only be decrypted with its corresponding key. Thus if a message or data stream were encrypted with the server’s private key, it can be decrypted only using its corresponding public key, ensuring that the data only could have come from the server.